12/5/2013 9:24 AM PST

The woman who claims she was raped by Florida State QB Jameis Winston says they were boozing at a local bar before the incident ... and she had 5 or 6 shots, this according to police documents.

According to a search warrant affidavit, the woman told cops she "began to feel the effects of the drinks" and was then whisked to a nearby apartment, where she was raped.

According to the affidavit, “[the accuser] then remembers entering an apartment on the ground floor. She remembers the male taking off her clothes then engaging in penile/vaginal sex with her as she told him to stop and tried to fight him off.”

Cops said in the affidavit ... at some point during the incident, another black male with dreadlocks came into the room and told the man to stop ... at which point he took the accuser into a nearby bathroom where he "completed the act."

Cops say the woman contacted police within an hour of the alleged rape -- but claim the accuser was so drunk at the time, she was "unable to tell a detective where the incident occurred."

She had only "hazy recollections of details after that," the cops said.

It wasn't until roughly 5 weeks after the incident that the woman first identified Winston as her attacker.

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